Coordinate-invariant incremental Lyapunov functions

Details Coordinate-invariant incremental Lyapunov functions Coordinate-invariant incremental Lyapunov functions

2011-07-13

arxiv.org/abs/1107.2681v2

Mathematics

Optimization and Control

8 pages. arXiv admin note: repeats content from arXiv:1005.4957

Scientific paper

The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, trajectories converge to each other, rather than to an equilibrium point or a particular trajectory. Similarly to stability, Lyapunov functions play an important role in the study of incremental stability. In this paper, we propose coordinate-invariant notions of incremental Lyapunov function and provide characterizations of incremental stability in terms of existence of the proposed Lyapunov functions.

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